| java.lang.Object
 java.lang.Math
| Math | | final public class Math (Code) | | The class
Math contains methods for performing basic
numeric operations such as the elementary exponential, logarithm,
square root, and trigonometric functions.
Unlike some of the numeric methods of class
StrictMath , all implementations of the equivalent
functions of class
Math are not defined to return the
bit-for-bit same results. This relaxation permits
better-performing implementations where strict reproducibility is
not required.
By default many of the
Math methods simply call
the equivalent method in
StrictMath for their
implementation. Code generators are encouraged to use
platform-specific native libraries or microprocessor instructions,
where available, to provide higher-performance implementations of
Math methods. Such higher-performance
implementations still must conform to the specification for
Math .
The quality of implementation specifications concern two
properties, accuracy of the returned result and monotonicity of the
method. Accuracy of the floating-point
Math methods
is measured in terms of ulps, units in the last place. For
a given floating-point format, an ulp of a specific real number
value is the distance between the two floating-point values
bracketing that numerical value. When discussing the accuracy of a
method as a whole rather than at a specific argument, the number of
ulps cited is for the worst-case error at any argument. If a
method always has an error less than 0.5 ulps, the method always
returns the floating-point number nearest the exact result; such a
method is correctly rounded. A correctly rounded method is
generally the best a floating-point approximation can be; however,
it is impractical for many floating-point methods to be correctly
rounded. Instead, for the
Math class, a larger error
bound of 1 or 2 ulps is allowed for certain methods. Informally,
with a 1 ulp error bound, when the exact result is a representable
number, the exact result should be returned as the computed result;
otherwise, either of the two floating-point values which bracket
the exact result may be returned. For exact results large in
magnitude, one of the endpoints of the bracket may be infinite.
Besides accuracy at individual arguments, maintaining proper
relations between the method at different arguments is also
important. Therefore, most methods with more than 0.5 ulp errors
are required to be semi-monotonic: whenever the mathematical
function is non-decreasing, so is the floating-point approximation,
likewise, whenever the mathematical function is non-increasing, so
is the floating-point approximation. Not all approximations that
have 1 ulp accuracy will automatically meet the monotonicity
requirements.
author:
unascribed
author:
Joseph D. Darcy
version:
1.80, 06/20/07
since:
JDK1.0 |
| Field Summary | |
| final public static double | E
The
double value that is closer than any other to
e, the base of the natural logarithms. | | final public static double | PI
The
double value that is closer than any other to
pi, the ratio of the circumference of a circle to its
diameter. |
| Method Summary | |
| public static double | IEEEremainder(double f1, double f2)
Computes the remainder operation on two arguments as prescribed
by the IEEE 754 standard.
The remainder value is mathematically equal to
f1 - f2 × n,
where n is the mathematical integer closest to the exact
mathematical value of the quotient
f1/f2 , and if two
mathematical integers are equally close to
f1/f2 ,
then n is the integer that is even. | | public static int | abs(int a)
Returns the absolute value of an
int value.
If the argument is not negative, the argument is returned.
If the argument is negative, the negation of the argument is returned. | | public static long | abs(long a)
Returns the absolute value of a
long value.
If the argument is not negative, the argument is returned.
If the argument is negative, the negation of the argument is returned. | | public static float | abs(float a)
Returns the absolute value of a
float value.
If the argument is not negative, the argument is returned.
If the argument is negative, the negation of the argument is returned.
Special cases:
- If the argument is positive zero or negative zero, the
result is positive zero.
| | public static double | abs(double a)
Returns the absolute value of a
double value.
If the argument is not negative, the argument is returned.
If the argument is negative, the negation of the argument is returned.
Special cases:
- If the argument is positive zero or negative zero, the result
is positive zero.
| | public static double | acos(double a)
Returns the arc cosine of a value; the returned angle is in the
range 0.0 through pi. | | public static double | asin(double a)
Returns the arc sine of a value; the returned angle is in the
range -pi/2 through pi/2. | | public static double | atan(double a)
Returns the arc tangent of a value; the returned angle is in the
range -pi/2 through pi/2. | | public static double | atan2(double y, double x)
Returns the angle theta from the conversion of rectangular
coordinates (
x ,
y ) to polar
coordinates (r, theta).
This method computes the phase theta by computing an arc tangent
of
y/x in the range of -pi to pi. | | public static double | cbrt(double a)
Returns the cube root of a
double value. | | public static double | ceil(double a)
Returns the smallest (closest to negative infinity)
double value that is greater than or equal to the
argument and is equal to a mathematical integer. | | public static double | copySign(double magnitude, double sign)
Returns the first floating-point argument with the sign of the
second floating-point argument. | | public static float | copySign(float magnitude, float sign)
Returns the first floating-point argument with the sign of the
second floating-point argument. | | public static double | cos(double a)
Returns the trigonometric cosine of an angle. | | public static double | cosh(double x)
Returns the hyperbolic cosine of a
double value.
The hyperbolic cosine of x is defined to be
(ex + e-x)/2
where e is
.
Special cases:
- If the argument is NaN, then the result is NaN.
- If the argument is infinite, then the result is positive
infinity.
- If the argument is zero, then the result is
1.0 .
The computed result must be within 2.5 ulps of the exact result.
Parameters:
x - The number whose hyperbolic cosine is to be returned. | | public static double | exp(double a)
Returns Euler's number e raised to the power of a
double value. | | public static double | expm1(double x)
Returns ex -1. | | public static double | floor(double a)
Returns the largest (closest to positive infinity)
double value that is less than or equal to the
argument and is equal to a mathematical integer. | | public static int | getExponent(float f)
Returns the unbiased exponent used in the representation of a
float . | | public static int | getExponent(double d)
Returns the unbiased exponent used in the representation of a
double . | | public static double | hypot(double x, double y)
Returns sqrt(x2 +y2)
without intermediate overflow or underflow.
Special cases:
- If either argument is infinite, then the result
is positive infinity.
- If either argument is NaN and neither argument is infinite,
then the result is NaN.
The computed result must be within 1 ulp of the exact
result. | | public static double | log(double a)
Returns the natural logarithm (base e) of a
double value. | | public static double | log10(double a)
Returns the base 10 logarithm of a
double value. | | public static double | log1p(double x)
Returns the natural logarithm of the sum of the argument and 1. | | public static int | max(int a, int b)
Returns the greater of two
int values. | | public static long | max(long a, long b)
Returns the greater of two
long values. | | public static float | max(float a, float b)
Returns the greater of two
float values. | | public static double | max(double a, double b)
Returns the greater of two
double values. | | public static int | min(int a, int b)
Returns the smaller of two
int values. | | public static long | min(long a, long b)
Returns the smaller of two
long values. | | public static float | min(float a, float b)
Returns the smaller of two
float values. | | public static double | min(double a, double b)
Returns the smaller of two
double values. | | public static double | nextAfter(double start, double direction)
Returns the floating-point number adjacent to the first
argument in the direction of the second argument. | | public static float | nextAfter(float start, double direction)
Returns the floating-point number adjacent to the first
argument in the direction of the second argument. | | public static double | nextUp(double d)
Returns the floating-point value adjacent to
d in
the direction of positive infinity. | | public static float | nextUp(float f)
Returns the floating-point value adjacent to
f in
the direction of positive infinity. | | public static double | pow(double a, double b)
Returns the value of the first argument raised to the power of the
second argument. | | public static double | random()
Returns a
double value with a positive sign, greater
than or equal to
0.0 and less than
1.0 . | | public static double | rint(double a)
Returns the
double value that is closest in value
to the argument and is equal to a mathematical integer. | | public static int | round(float a)
Returns the closest
int to the argument. | | public static long | round(double a)
Returns the closest
long to the argument. | | public static double | scalb(double d, int scaleFactor)
Return
d ×
2
scaleFactor rounded as if performed
by a single correctly rounded floating-point multiply to a
member of the double value set. | | public static float | scalb(float f, int scaleFactor)
Return
f ×
2
scaleFactor rounded as if performed
by a single correctly rounded floating-point multiply to a
member of the float value set. | | public static double | signum(double d)
Returns the signum function of the argument; zero if the argument
is zero, 1.0 if the argument is greater than zero, -1.0 if the
argument is less than zero.
Special Cases:
- If the argument is NaN, then the result is NaN.
- If the argument is positive zero or negative zero, then the
result is the same as the argument.
Parameters:
d - the floating-point value whose signum is to be returned the signum function of the argument
author:
Joseph D. | | public static float | signum(float f)
Returns the signum function of the argument; zero if the argument
is zero, 1.0f if the argument is greater than zero, -1.0f if the
argument is less than zero.
Special Cases:
- If the argument is NaN, then the result is NaN.
- If the argument is positive zero or negative zero, then the
result is the same as the argument.
Parameters:
f - the floating-point value whose signum is to be returned the signum function of the argument
author:
Joseph D. | | public static double | sin(double a)
Returns the trigonometric sine of an angle. | | public static double | sinh(double x)
Returns the hyperbolic sine of a
double value.
The hyperbolic sine of x is defined to be
(ex - e-x)/2
where e is
.
Special cases:
- If the argument is NaN, then the result is NaN.
- If the argument is infinite, then the result is an infinity
with the same sign as the argument.
- If the argument is zero, then the result is a zero with the
same sign as the argument.
The computed result must be within 2.5 ulps of the exact result.
Parameters:
x - The number whose hyperbolic sine is to be returned. | | public static double | sqrt(double a)
Returns the correctly rounded positive square root of a
double value.
Special cases:
- If the argument is NaN or less than zero, then the result
is NaN.
| | public static double | tan(double a)
Returns the trigonometric tangent of an angle. | | public static double | tanh(double x)
Returns the hyperbolic tangent of a
double value.
The hyperbolic tangent of x is defined to be
(ex - e-x)/(ex + e-x),
in other words,
/
. | | public static double | toDegrees(double angrad)
Converts an angle measured in radians to an approximately
equivalent angle measured in degrees. | | public static double | toRadians(double angdeg)
Converts an angle measured in degrees to an approximately
equivalent angle measured in radians. | | public static double | ulp(double d)
Returns the size of an ulp of the argument. | | public static float | ulp(float f)
Returns the size of an ulp of the argument. |
| E | | final public static double E(Code) | | The
double value that is closer than any other to
e, the base of the natural logarithms.
|
| PI | | final public static double PI(Code) | | The
double value that is closer than any other to
pi, the ratio of the circumference of a circle to its
diameter.
|
| IEEEremainder | | public static double IEEEremainder(double f1, double f2)(Code) | | Computes the remainder operation on two arguments as prescribed
by the IEEE 754 standard.
The remainder value is mathematically equal to
f1 - f2 × n,
where n is the mathematical integer closest to the exact
mathematical value of the quotient
f1/f2 , and if two
mathematical integers are equally close to
f1/f2 ,
then n is the integer that is even. If the remainder is
zero, its sign is the same as the sign of the first argument.
Special cases:
- If either argument is NaN, or the first argument is infinite,
or the second argument is positive zero or negative zero, then the
result is NaN.
- If the first argument is finite and the second argument is
infinite, then the result is the same as the first argument.
Parameters:
f1 - the dividend.
Parameters:
f2 - the divisor. the remainder when f1 is divided by f2 . |
| abs | | public static int abs(int a)(Code) | | Returns the absolute value of an
int value.
If the argument is not negative, the argument is returned.
If the argument is negative, the negation of the argument is returned.
Note that if the argument is equal to the value of
Integer.MIN_VALUE , the most negative representable
int value, the result is that same value, which is
negative.
Parameters:
a - the argument whose absolute value is to be determined the absolute value of the argument. |
| abs | | public static long abs(long a)(Code) | | Returns the absolute value of a
long value.
If the argument is not negative, the argument is returned.
If the argument is negative, the negation of the argument is returned.
Note that if the argument is equal to the value of
Long.MIN_VALUE , the most negative representable
long value, the result is that same value, which
is negative.
Parameters:
a - the argument whose absolute value is to be determined the absolute value of the argument. |
| abs | | public static float abs(float a)(Code) | | Returns the absolute value of a
float value.
If the argument is not negative, the argument is returned.
If the argument is negative, the negation of the argument is returned.
Special cases:
- If the argument is positive zero or negative zero, the
result is positive zero.
- If the argument is infinite, the result is positive infinity.
- If the argument is NaN, the result is NaN.
In other words, the result is the same as the value of the expression:
Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))
Parameters:
a - the argument whose absolute value is to be determined the absolute value of the argument. |
| abs | | public static double abs(double a)(Code) | | Returns the absolute value of a
double value.
If the argument is not negative, the argument is returned.
If the argument is negative, the negation of the argument is returned.
Special cases:
- If the argument is positive zero or negative zero, the result
is positive zero.
- If the argument is infinite, the result is positive infinity.
- If the argument is NaN, the result is NaN.
In other words, the result is the same as the value of the expression:
Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)
Parameters:
a - the argument whose absolute value is to be determined the absolute value of the argument. |
| acos | | public static double acos(double a)(Code) | | Returns the arc cosine of a value; the returned angle is in the
range 0.0 through pi. Special case:
- If the argument is NaN or its absolute value is greater
than 1, then the result is NaN.
The computed result must be within 1 ulp of the exact result.
Results must be semi-monotonic.
Parameters:
a - the value whose arc cosine is to be returned. the arc cosine of the argument. |
| asin | | public static double asin(double a)(Code) | | Returns the arc sine of a value; the returned angle is in the
range -pi/2 through pi/2. Special cases:
- If the argument is NaN or its absolute value is greater
than 1, then the result is NaN.
- If the argument is zero, then the result is a zero with the
same sign as the argument.
The computed result must be within 1 ulp of the exact result.
Results must be semi-monotonic.
Parameters:
a - the value whose arc sine is to be returned. the arc sine of the argument. |
| atan | | public static double atan(double a)(Code) | | Returns the arc tangent of a value; the returned angle is in the
range -pi/2 through pi/2. Special cases:
- If the argument is NaN, then the result is NaN.
- If the argument is zero, then the result is a zero with the
same sign as the argument.
The computed result must be within 1 ulp of the exact result.
Results must be semi-monotonic.
Parameters:
a - the value whose arc tangent is to be returned. the arc tangent of the argument. |
| atan2 | | public static double atan2(double y, double x)(Code) | | Returns the angle theta from the conversion of rectangular
coordinates (
x ,
y ) to polar
coordinates (r, theta).
This method computes the phase theta by computing an arc tangent
of
y/x in the range of -pi to pi. Special
cases:
- If either argument is NaN, then the result is NaN.
- If the first argument is positive zero and the second argument
is positive, or the first argument is positive and finite and the
second argument is positive infinity, then the result is positive
zero.
- If the first argument is negative zero and the second argument
is positive, or the first argument is negative and finite and the
second argument is positive infinity, then the result is negative zero.
- If the first argument is positive zero and the second argument
is negative, or the first argument is positive and finite and the
second argument is negative infinity, then the result is the
double value closest to pi.
- If the first argument is negative zero and the second argument
is negative, or the first argument is negative and finite and the
second argument is negative infinity, then the result is the
double value closest to -pi.
- If the first argument is positive and the second argument is
positive zero or negative zero, or the first argument is positive
infinity and the second argument is finite, then the result is the
double value closest to pi/2.
- If the first argument is negative and the second argument is
positive zero or negative zero, or the first argument is negative
infinity and the second argument is finite, then the result is the
double value closest to -pi/2.
- If both arguments are positive infinity, then the result is the
double value closest to pi/4.
- If the first argument is positive infinity and the second argument
is negative infinity, then the result is the
double
value closest to 3*pi/4.
- If the first argument is negative infinity and the second argument
is positive infinity, then the result is the
double value
closest to -pi/4.
- If both arguments are negative infinity, then the result is the
double value closest to -3*pi/4.
The computed result must be within 2 ulps of the exact result.
Results must be semi-monotonic.
Parameters:
y - the ordinate coordinate
Parameters:
x - the abscissa coordinate the theta component of the point(r, theta)in polar coordinates that corresponds to the point(x, y) in Cartesian coordinates. |
| cbrt | | public static double cbrt(double a)(Code) | | Returns the cube root of a
double value. For
positive finite
x ,
cbrt(-x) == -cbrt(x) ; that is, the cube root of a negative value is
the negative of the cube root of that value's magnitude.
Special cases:
- If the argument is NaN, then the result is NaN.
- If the argument is infinite, then the result is an infinity
with the same sign as the argument.
- If the argument is zero, then the result is a zero with the
same sign as the argument.
The computed result must be within 1 ulp of the exact result.
Parameters:
a - a value. the cube root of a .
since:
1.5 |
| ceil | | public static double ceil(double a)(Code) | | Returns the smallest (closest to negative infinity)
double value that is greater than or equal to the
argument and is equal to a mathematical integer. Special cases:
- If the argument value is already equal to a
mathematical integer, then the result is the same as the
argument.
- If the argument is NaN or an infinity or
positive zero or negative zero, then the result is the same as
the argument.
- If the argument value is less than zero but
greater than -1.0, then the result is negative zero.
Note
that the value of
Math.ceil(x) is exactly the
value of
-Math.floor(-x) .
Parameters:
a - a value. the smallest (closest to negative infinity) floating-point value that is greater than or equal to the argument and is equal to a mathematical integer. |
| copySign | | public static double copySign(double magnitude, double sign)(Code) | | Returns the first floating-point argument with the sign of the
second floating-point argument. Note that unlike the
StrictMath.copySign(doubledouble) StrictMath.copySign method, this method does not require NaN
sign arguments to be treated as positive values; implementations are
permitted to treat some NaN arguments as positive and other NaN
arguments as negative to allow greater performance.
Parameters:
magnitude - the parameter providing the magnitude of the result
Parameters:
sign - the parameter providing the sign of the result a value with the magnitude of magnitude and the sign of sign .
since:
1.6 |
| copySign | | public static float copySign(float magnitude, float sign)(Code) | | Returns the first floating-point argument with the sign of the
second floating-point argument. Note that unlike the
StrictMath.copySign(floatfloat) StrictMath.copySign method, this method does not require NaN
sign arguments to be treated as positive values; implementations are
permitted to treat some NaN arguments as positive and other NaN
arguments as negative to allow greater performance.
Parameters:
magnitude - the parameter providing the magnitude of the result
Parameters:
sign - the parameter providing the sign of the result a value with the magnitude of magnitude and the sign of sign .
since:
1.6 |
| cos | | public static double cos(double a)(Code) | | Returns the trigonometric cosine of an angle. Special cases:
- If the argument is NaN or an infinity, then the
result is NaN.
The computed result must be within 1 ulp of the exact result.
Results must be semi-monotonic.
Parameters:
a - an angle, in radians. the cosine of the argument. |
| cosh | | public static double cosh(double x)(Code) | | Returns the hyperbolic cosine of a
double value.
The hyperbolic cosine of x is defined to be
(ex + e-x)/2
where e is
.
Special cases:
- If the argument is NaN, then the result is NaN.
- If the argument is infinite, then the result is positive
infinity.
- If the argument is zero, then the result is
1.0 .
The computed result must be within 2.5 ulps of the exact result.
Parameters:
x - The number whose hyperbolic cosine is to be returned. The hyperbolic cosine of x .
since:
1.5 |
| exp | | public static double exp(double a)(Code) | | Returns Euler's number e raised to the power of a
double value. Special cases:
- If the argument is NaN, the result is NaN.
- If the argument is positive infinity, then the result is
positive infinity.
- If the argument is negative infinity, then the result is
positive zero.
The computed result must be within 1 ulp of the exact result.
Results must be semi-monotonic.
Parameters:
a - the exponent to raise e to. the value e a , where e is the base of the natural logarithms. |
| expm1 | | public static double expm1(double x)(Code) | | Returns ex -1. Note that for values of
x near 0, the exact sum of
expm1(x) + 1 is much closer to the true
result of ex than
exp(x) .
Special cases:
- If the argument is NaN, the result is NaN.
- If the argument is positive infinity, then the result is
positive infinity.
- If the argument is negative infinity, then the result is
-1.0.
- If the argument is zero, then the result is a zero with the
same sign as the argument.
The computed result must be within 1 ulp of the exact result.
Results must be semi-monotonic. The result of
expm1 for any finite input must be greater than or
equal to
-1.0 . Note that once the exact result of
e
x - 1 is within 1/2
ulp of the limit value -1,
-1.0 should be
returned.
Parameters:
x - the exponent to raise e to in the computation ofe x -1. the value e x - 1.
since:
1.5 |
| floor | | public static double floor(double a)(Code) | | Returns the largest (closest to positive infinity)
double value that is less than or equal to the
argument and is equal to a mathematical integer. Special cases:
- If the argument value is already equal to a
mathematical integer, then the result is the same as the
argument.
- If the argument is NaN or an infinity or
positive zero or negative zero, then the result is the same as
the argument.
Parameters:
a - a value. the largest (closest to positive infinity) floating-point value that less than or equal to the argumentand is equal to a mathematical integer. |
| getExponent | | public static int getExponent(float f)(Code) | | Returns the unbiased exponent used in the representation of a
float . Special cases:
Parameters:
f - a float value the unbiased exponent of the argument
since:
1.6 |
| getExponent | | public static int getExponent(double d)(Code) | | Returns the unbiased exponent used in the representation of a
double . Special cases:
Parameters:
d - a double value the unbiased exponent of the argument
since:
1.6 |
| hypot | | public static double hypot(double x, double y)(Code) | | Returns sqrt(x2 +y2)
without intermediate overflow or underflow.
Special cases:
- If either argument is infinite, then the result
is positive infinity.
- If either argument is NaN and neither argument is infinite,
then the result is NaN.
The computed result must be within 1 ulp of the exact
result. If one parameter is held constant, the results must be
semi-monotonic in the other parameter.
Parameters:
x - a value
Parameters:
y - a value sqrt(x2 +y2)without intermediate overflow or underflow
since:
1.5 |
| log | | public static double log(double a)(Code) | | Returns the natural logarithm (base e) of a
double value. Special cases:
- If the argument is NaN or less than zero, then the result
is NaN.
- If the argument is positive infinity, then the result is
positive infinity.
- If the argument is positive zero or negative zero, then the
result is negative infinity.
The computed result must be within 1 ulp of the exact result.
Results must be semi-monotonic.
Parameters:
a - a value the value ln a , the natural logarithm of a . |
| log10 | | public static double log10(double a)(Code) | | Returns the base 10 logarithm of a
double value.
Special cases:
- If the argument is NaN or less than zero, then the result
is NaN.
- If the argument is positive infinity, then the result is
positive infinity.
- If the argument is positive zero or negative zero, then the
result is negative infinity.
- If the argument is equal to 10n for
integer n, then the result is n.
The computed result must be within 1 ulp of the exact result.
Results must be semi-monotonic.
Parameters:
a - a value the base 10 logarithm of a .
since:
1.5 |
| log1p | | public static double log1p(double x)(Code) | | Returns the natural logarithm of the sum of the argument and 1.
Note that for small values
x , the result of
log1p(x) is much closer to the true result of ln(1
+
x ) than the floating-point evaluation of
log(1.0+x) .
Special cases:
- If the argument is NaN or less than -1, then the result is
NaN.
- If the argument is positive infinity, then the result is
positive infinity.
- If the argument is negative one, then the result is
negative infinity.
- If the argument is zero, then the result is a zero with the
same sign as the argument.
The computed result must be within 1 ulp of the exact result.
Results must be semi-monotonic.
Parameters:
x - a value the value ln( x + 1), the naturallog of x + 1
since:
1.5 |
| max | | public static int max(int a, int b)(Code) | | Returns the greater of two
int values. That is, the
result is the argument closer to the value of
Integer.MAX_VALUE . If the arguments have the same value,
the result is that same value.
Parameters:
a - an argument.
Parameters:
b - another argument. the larger of a and b . |
| max | | public static long max(long a, long b)(Code) | | Returns the greater of two
long values. That is, the
result is the argument closer to the value of
Long.MAX_VALUE . If the arguments have the same value,
the result is that same value.
Parameters:
a - an argument.
Parameters:
b - another argument. the larger of a and b . |
| max | | public static float max(float a, float b)(Code) | | Returns the greater of two
float values. That is,
the result is the argument closer to positive infinity. If the
arguments have the same value, the result is that same
value. If either value is NaN, then the result is NaN. Unlike
the numerical comparison operators, this method considers
negative zero to be strictly smaller than positive zero. If one
argument is positive zero and the other negative zero, the
result is positive zero.
Parameters:
a - an argument.
Parameters:
b - another argument. the larger of a and b . |
| max | | public static double max(double a, double b)(Code) | | Returns the greater of two
double values. That
is, the result is the argument closer to positive infinity. If
the arguments have the same value, the result is that same
value. If either value is NaN, then the result is NaN. Unlike
the numerical comparison operators, this method considers
negative zero to be strictly smaller than positive zero. If one
argument is positive zero and the other negative zero, the
result is positive zero.
Parameters:
a - an argument.
Parameters:
b - another argument. the larger of a and b . |
| min | | public static int min(int a, int b)(Code) | | Returns the smaller of two
int values. That is,
the result the argument closer to the value of
Integer.MIN_VALUE . If the arguments have the same
value, the result is that same value.
Parameters:
a - an argument.
Parameters:
b - another argument. the smaller of a and b . |
| min | | public static long min(long a, long b)(Code) | | Returns the smaller of two
long values. That is,
the result is the argument closer to the value of
Long.MIN_VALUE . If the arguments have the same
value, the result is that same value.
Parameters:
a - an argument.
Parameters:
b - another argument. the smaller of a and b . |
| min | | public static float min(float a, float b)(Code) | | Returns the smaller of two
float values. That is,
the result is the value closer to negative infinity. If the
arguments have the same value, the result is that same
value. If either value is NaN, then the result is NaN. Unlike
the numerical comparison operators, this method considers
negative zero to be strictly smaller than positive zero. If
one argument is positive zero and the other is negative zero,
the result is negative zero.
Parameters:
a - an argument.
Parameters:
b - another argument. the smaller of a and b . |
| min | | public static double min(double a, double b)(Code) | | Returns the smaller of two
double values. That
is, the result is the value closer to negative infinity. If the
arguments have the same value, the result is that same
value. If either value is NaN, then the result is NaN. Unlike
the numerical comparison operators, this method considers
negative zero to be strictly smaller than positive zero. If one
argument is positive zero and the other is negative zero, the
result is negative zero.
Parameters:
a - an argument.
Parameters:
b - another argument. the smaller of a and b . |
| nextAfter | | public static double nextAfter(double start, double direction)(Code) | | Returns the floating-point number adjacent to the first
argument in the direction of the second argument. If both
arguments compare as equal the second argument is returned.
Special cases:
- If either argument is a NaN, then NaN is returned.
- If both arguments are signed zeros,
direction is returned unchanged (as implied by the requirement of
returning the second argument if the arguments compare as
equal).
- If
start is
±
Double.MIN_VALUE and
direction has a value such that the result should have a smaller
magnitude, then a zero with the same sign as
start is returned.
- If
start is infinite and
direction has a value such that the result should
have a smaller magnitude,
Double.MAX_VALUE with the
same sign as
start is returned.
- If
start is equal to ±
Double.MAX_VALUE and
direction has a
value such that the result should have a larger magnitude, an
infinity with same sign as
start is returned.
Parameters:
start - starting floating-point value
Parameters:
direction - value indicating which of start 's neighbors or start shouldbe returned The floating-point number adjacent to start in thedirection of direction .
since:
1.6 |
| nextAfter | | public static float nextAfter(float start, double direction)(Code) | | Returns the floating-point number adjacent to the first
argument in the direction of the second argument. If both
arguments compare as equal a value equivalent to the second argument
is returned.
Special cases:
- If either argument is a NaN, then NaN is returned.
- If both arguments are signed zeros, a value equivalent
to
direction is returned.
- If
start is
±
Float.MIN_VALUE and
direction has a value such that the result should have a smaller
magnitude, then a zero with the same sign as
start is returned.
- If
start is infinite and
direction has a value such that the result should
have a smaller magnitude,
Float.MAX_VALUE with the
same sign as
start is returned.
- If
start is equal to ±
Float.MAX_VALUE and
direction has a
value such that the result should have a larger magnitude, an
infinity with same sign as
start is returned.
Parameters:
start - starting floating-point value
Parameters:
direction - value indicating which of start 's neighbors or start shouldbe returned The floating-point number adjacent to start in thedirection of direction .
since:
1.6 |
| nextUp | | public static double nextUp(double d)(Code) | | Returns the floating-point value adjacent to
d in
the direction of positive infinity. This method is
semantically equivalent to
nextAfter(d, Double.POSITIVE_INFINITY) ; however, a
nextUp implementation may run faster than its equivalent
nextAfter call.
Special Cases:
- If the argument is NaN, the result is NaN.
- If the argument is positive infinity, the result is
positive infinity.
- If the argument is zero, the result is
Double.MIN_VALUE
Parameters:
d - starting floating-point value The adjacent floating-point value closer to positiveinfinity.
since:
1.6 |
| nextUp | | public static float nextUp(float f)(Code) | | Returns the floating-point value adjacent to
f in
the direction of positive infinity. This method is
semantically equivalent to
nextAfter(f, Float.POSITIVE_INFINITY) ; however, a
nextUp implementation may run faster than its equivalent
nextAfter call.
Special Cases:
- If the argument is NaN, the result is NaN.
- If the argument is positive infinity, the result is
positive infinity.
- If the argument is zero, the result is
Float.MIN_VALUE
Parameters:
f - starting floating-point value The adjacent floating-point value closer to positiveinfinity.
since:
1.6 |
| pow | | public static double pow(double a, double b)(Code) | | Returns the value of the first argument raised to the power of the
second argument. Special cases:
- If the second argument is positive or negative zero, then the
result is 1.0.
- If the second argument is 1.0, then the result is the same as the
first argument.
- If the second argument is NaN, then the result is NaN.
- If the first argument is NaN and the second argument is nonzero,
then the result is NaN.
- If
- the absolute value of the first argument is greater than 1
and the second argument is positive infinity, or
- the absolute value of the first argument is less than 1 and
the second argument is negative infinity,
then the result is positive infinity.
- If
- the absolute value of the first argument is greater than 1 and
the second argument is negative infinity, or
- the absolute value of the
first argument is less than 1 and the second argument is positive
infinity,
then the result is positive zero.
- If the absolute value of the first argument equals 1 and the
second argument is infinite, then the result is NaN.
- If
- the first argument is positive zero and the second argument
is greater than zero, or
- the first argument is positive infinity and the second
argument is less than zero,
then the result is positive zero.
- If
- the first argument is positive zero and the second argument
is less than zero, or
- the first argument is positive infinity and the second
argument is greater than zero,
then the result is positive infinity.
- If
- the first argument is negative zero and the second argument
is greater than zero but not a finite odd integer, or
- the first argument is negative infinity and the second
argument is less than zero but not a finite odd integer,
then the result is positive zero.
- If
- the first argument is negative zero and the second argument
is a positive finite odd integer, or
- the first argument is negative infinity and the second
argument is a negative finite odd integer,
then the result is negative zero.
- If
- the first argument is negative zero and the second argument
is less than zero but not a finite odd integer, or
- the first argument is negative infinity and the second
argument is greater than zero but not a finite odd integer,
then the result is positive infinity.
- If
- the first argument is negative zero and the second argument
is a negative finite odd integer, or
- the first argument is negative infinity and the second
argument is a positive finite odd integer,
then the result is negative infinity.
- If the first argument is finite and less than zero
- if the second argument is a finite even integer, the
result is equal to the result of raising the absolute value of
the first argument to the power of the second argument
- if the second argument is a finite odd integer, the result
is equal to the negative of the result of raising the absolute
value of the first argument to the power of the second
argument
- if the second argument is finite and not an integer, then
the result is NaN.
- If both arguments are integers, then the result is exactly equal
to the mathematical result of raising the first argument to the power
of the second argument if that result can in fact be represented
exactly as a
double value.
(In the foregoing descriptions, a floating-point value is
considered to be an integer if and only if it is finite and a
fixed point of the method
Math.ceil ceil or,
equivalently, a fixed point of the method
Math.floorfloor . A value is a fixed point of a one-argument
method if and only if the result of applying the method to the
value is equal to the value.)
The computed result must be within 1 ulp of the exact result.
Results must be semi-monotonic.
Parameters:
a - the base.
Parameters:
b - the exponent. the value a b . |
| random | | public static double random()(Code) | | Returns a
double value with a positive sign, greater
than or equal to
0.0 and less than
1.0 .
Returned values are chosen pseudorandomly with (approximately)
uniform distribution from that range.
When this method is first called, it creates a single new
pseudorandom-number generator, exactly as if by the expression
new java.util.Random This
new pseudorandom-number generator is used thereafter for all
calls to this method and is used nowhere else.
This method is properly synchronized to allow correct use by
more than one thread. However, if many threads need to generate
pseudorandom numbers at a great rate, it may reduce contention
for each thread to have its own pseudorandom-number generator.
a pseudorandom double greater than or equal to 0.0 and less than 1.0 .
See Also: java.util.Random.nextDouble |
| rint | | public static double rint(double a)(Code) | | Returns the
double value that is closest in value
to the argument and is equal to a mathematical integer. If two
double values that are mathematical integers are
equally close, the result is the integer value that is
even. Special cases:
- If the argument value is already equal to a mathematical
integer, then the result is the same as the argument.
- If the argument is NaN or an infinity or positive zero or negative
zero, then the result is the same as the argument.
Parameters:
a - a double value. the closest floating-point value to a that isequal to a mathematical integer. |
| round | | public static int round(float a)(Code) | | Returns the closest
int to the argument. The
result is rounded to an integer by adding 1/2, taking the
floor of the result, and casting the result to type
int .
In other words, the result is equal to the value of the expression:
(int)Math.floor(a + 0.5f)
Special cases:
- If the argument is NaN, the result is 0.
- If the argument is negative infinity or any value less than or
equal to the value of
Integer.MIN_VALUE , the result is
equal to the value of
Integer.MIN_VALUE .
- If the argument is positive infinity or any value greater than or
equal to the value of
Integer.MAX_VALUE , the result is
equal to the value of
Integer.MAX_VALUE .
Parameters:
a - a floating-point value to be rounded to an integer. the value of the argument rounded to the nearest int value.
See Also: java.lang.Integer.MAX_VALUE
See Also: java.lang.Integer.MIN_VALUE |
| round | | public static long round(double a)(Code) | | Returns the closest
long to the argument. The result
is rounded to an integer by adding 1/2, taking the floor of the
result, and casting the result to type
long . In other
words, the result is equal to the value of the expression:
(long)Math.floor(a + 0.5d)
Special cases:
- If the argument is NaN, the result is 0.
- If the argument is negative infinity or any value less than or
equal to the value of
Long.MIN_VALUE , the result is
equal to the value of
Long.MIN_VALUE .
- If the argument is positive infinity or any value greater than or
equal to the value of
Long.MAX_VALUE , the result is
equal to the value of
Long.MAX_VALUE .
Parameters:
a - a floating-point value to be rounded to a long . the value of the argument rounded to the nearest long value.
See Also: java.lang.Long.MAX_VALUE
See Also: java.lang.Long.MIN_VALUE |
| scalb | | public static double scalb(double d, int scaleFactor)(Code) | | Return
d ×
2
scaleFactor rounded as if performed
by a single correctly rounded floating-point multiply to a
member of the double value set. See the Java
Language Specification for a discussion of floating-point
value sets. If the exponent of the result is between
Double.MIN_EXPONENT and
Double.MAX_EXPONENT , the
answer is calculated exactly. If the exponent of the result
would be larger than
Double.MAX_EXPONENT , an
infinity is returned. Note that if the result is subnormal,
precision may be lost; that is, when
scalb(x, n) is subnormal,
scalb(scalb(x, n), -n) may not equal
x. When the result is non-NaN, the result has the same
sign as
d .
Special cases:
- If the first argument is NaN, NaN is returned.
- If the first argument is infinite, then an infinity of the
same sign is returned.
- If the first argument is zero, then a zero of the same
sign is returned.
Parameters:
d - number to be scaled by a power of two.
Parameters:
scaleFactor - power of 2 used to scale d d × 2 scaleFactor
since:
1.6 |
| scalb | | public static float scalb(float f, int scaleFactor)(Code) | | Return
f ×
2
scaleFactor rounded as if performed
by a single correctly rounded floating-point multiply to a
member of the float value set. See the Java
Language Specification for a discussion of floating-point
value sets. If the exponent of the result is between
Float.MIN_EXPONENT and
Float.MAX_EXPONENT , the
answer is calculated exactly. If the exponent of the result
would be larger than
Float.MAX_EXPONENT , an
infinity is returned. Note that if the result is subnormal,
precision may be lost; that is, when
scalb(x, n) is subnormal,
scalb(scalb(x, n), -n) may not equal
x. When the result is non-NaN, the result has the same
sign as
f .
Special cases:
- If the first argument is NaN, NaN is returned.
- If the first argument is infinite, then an infinity of the
same sign is returned.
- If the first argument is zero, then a zero of the same
sign is returned.
Parameters:
f - number to be scaled by a power of two.
Parameters:
scaleFactor - power of 2 used to scale f f × 2 scaleFactor
since:
1.6 |
| signum | | public static double signum(double d)(Code) | | Returns the signum function of the argument; zero if the argument
is zero, 1.0 if the argument is greater than zero, -1.0 if the
argument is less than zero.
Special Cases:
- If the argument is NaN, then the result is NaN.
- If the argument is positive zero or negative zero, then the
result is the same as the argument.
Parameters:
d - the floating-point value whose signum is to be returned the signum function of the argument
author:
Joseph D. Darcy
since:
1.5 |
| signum | | public static float signum(float f)(Code) | | Returns the signum function of the argument; zero if the argument
is zero, 1.0f if the argument is greater than zero, -1.0f if the
argument is less than zero.
Special Cases:
- If the argument is NaN, then the result is NaN.
- If the argument is positive zero or negative zero, then the
result is the same as the argument.
Parameters:
f - the floating-point value whose signum is to be returned the signum function of the argument
author:
Joseph D. Darcy
since:
1.5 |
| sin | | public static double sin(double a)(Code) | | Returns the trigonometric sine of an angle. Special cases:
- If the argument is NaN or an infinity, then the
result is NaN.
- If the argument is zero, then the result is a zero with the
same sign as the argument.
The computed result must be within 1 ulp of the exact result.
Results must be semi-monotonic.
Parameters:
a - an angle, in radians. the sine of the argument. |
| sinh | | public static double sinh(double x)(Code) | | Returns the hyperbolic sine of a
double value.
The hyperbolic sine of x is defined to be
(ex - e-x)/2
where e is
.
Special cases:
- If the argument is NaN, then the result is NaN.
- If the argument is infinite, then the result is an infinity
with the same sign as the argument.
- If the argument is zero, then the result is a zero with the
same sign as the argument.
The computed result must be within 2.5 ulps of the exact result.
Parameters:
x - The number whose hyperbolic sine is to be returned. The hyperbolic sine of x .
since:
1.5 |
| sqrt | | public static double sqrt(double a)(Code) | | Returns the correctly rounded positive square root of a
double value.
Special cases:
- If the argument is NaN or less than zero, then the result
is NaN.
- If the argument is positive infinity, then the result is positive
infinity.
- If the argument is positive zero or negative zero, then the
result is the same as the argument.
Otherwise, the result is the
double value closest to
the true mathematical square root of the argument value.
Parameters:
a - a value. the positive square root of a .If the argument is NaN or less than zero, the result is NaN. |
| tan | | public static double tan(double a)(Code) | | Returns the trigonometric tangent of an angle. Special cases:
- If the argument is NaN or an infinity, then the result
is NaN.
- If the argument is zero, then the result is a zero with the
same sign as the argument.
The computed result must be within 1 ulp of the exact result.
Results must be semi-monotonic.
Parameters:
a - an angle, in radians. the tangent of the argument. |
| tanh | | public static double tanh(double x)(Code) | | Returns the hyperbolic tangent of a
double value.
The hyperbolic tangent of x is defined to be
(ex - e-x)/(ex + e-x),
in other words,
/
. Note
that the absolute value of the exact tanh is always less than
1.
Special cases:
- If the argument is NaN, then the result is NaN.
- If the argument is zero, then the result is a zero with the
same sign as the argument.
- If the argument is positive infinity, then the result is
+1.0 .
- If the argument is negative infinity, then the result is
-1.0 .
The computed result must be within 2.5 ulps of the exact result.
The result of
tanh for any finite input must have
an absolute value less than or equal to 1. Note that once the
exact result of tanh is within 1/2 of an ulp of the limit value
of ±1, correctly signed ±
1.0 should
be returned.
Parameters:
x - The number whose hyperbolic tangent is to be returned. The hyperbolic tangent of x .
since:
1.5 |
| toDegrees | | public static double toDegrees(double angrad)(Code) | | Converts an angle measured in radians to an approximately
equivalent angle measured in degrees. The conversion from
radians to degrees is generally inexact; users should
not expect
cos(toRadians(90.0)) to exactly
equal
0.0 .
Parameters:
angrad - an angle, in radians the measurement of the angle angrad in degrees.
since:
1.2 |
| toRadians | | public static double toRadians(double angdeg)(Code) | | Converts an angle measured in degrees to an approximately
equivalent angle measured in radians. The conversion from
degrees to radians is generally inexact.
Parameters:
angdeg - an angle, in degrees the measurement of the angle angdeg in radians.
since:
1.2 |
| ulp | | public static double ulp(double d)(Code) | | Returns the size of an ulp of the argument. An ulp of a
double value is the positive distance between this
floating-point value and the
double value next
larger in magnitude. Note that for non-NaN x,
ulp(-x) == ulp(x).
Special Cases:
- If the argument is NaN, then the result is NaN.
- If the argument is positive or negative infinity, then the
result is positive infinity.
- If the argument is positive or negative zero, then the result is
Double.MIN_VALUE .
- If the argument is ±
Double.MAX_VALUE , then
the result is equal to 2971.
Parameters:
d - the floating-point value whose ulp is to be returned the size of an ulp of the argument
author:
Joseph D. Darcy
since:
1.5 |
| ulp | | public static float ulp(float f)(Code) | | Returns the size of an ulp of the argument. An ulp of a
float value is the positive distance between this
floating-point value and the
float value next
larger in magnitude. Note that for non-NaN x,
ulp(-x) == ulp(x).
Special Cases:
- If the argument is NaN, then the result is NaN.
- If the argument is positive or negative infinity, then the
result is positive infinity.
- If the argument is positive or negative zero, then the result is
Float.MIN_VALUE .
- If the argument is ±
Float.MAX_VALUE , then
the result is equal to 2104.
Parameters:
f - the floating-point value whose ulp is to be returned the size of an ulp of the argument
author:
Joseph D. Darcy
since:
1.5 |
|
|